Is it possible to program Arduino UNO with USB/TTL adaptor without connecting the Vcc and GND pins (RX/TX and DTR only.)
As a minimum you need to add ground as well - even if the Mac is battery powered. Serial port signals are ground referenced so removing the ground would prevent operation.
Operation is possible without deriving Vcc from the USB port, but you will then need to derive Vcc from some other source.
If connecting ground alone causes your Mac to reset you have a serious system problem which may damage your Mac and which possibly may be dangerous to you.
Presumably you are NOT using an external power supply for the UNO.
In case you are: If the power supply for the UNO is AC mains powered it should be connected to the same mains outlet as the Mac. If the programmer powerpack is intended to be grounded but is not powered from a grounded socket AND using a 3 wire mains lead (ie with a ground pin and wire) then it s possible in some cases for the programmer to float at half mains voltage with a high impedance capacitive connection to mains. This is not usually dangerous to people but can cause minor nuisance shocks. It can destroy equipment (ask me how I know :-( .)
If you have a DMM (digital multimeter) set it to an AC voltage range greater than your local mains voltage and measure the AC voltage from a known ground (such as a water tap in most cases) and the programmer power supply (either wire or jack terminal). If you measure a voltage of about 50VAC with 100 VAC mains or about 115 VAC with 230 VAC mains then the power supply MUST be operated with a 3 wire mains cord and grounded power socket OR a ground lead from mains ground to power supply output ground.
If the Mac is battery powered and you have reset problems then something is wrong with connections or signal levels. You may be feeding voltage back onto the USB lines or loading the too heavily or ... ?